Approximation and Fast Calculation Tricks

Why approximation?

In RRB NTPC, many simplification questions have options far apart. Rounding numbers to convenient values saves time without losing accuracy.

Rules

1. Round to the nearest whole number, ten or hundred: 49.87 ≈ 50, 301.2 ≈ 300.
2. Round up one and down the other in multiplication to balance error: 49 × 21 ≈ 50 × 20 = 1000 (actual 1029).
3. Square roots: √168 ≈ √169 = 13. Cube roots: ∛730 ≈ 9.
4. Percentages: 24.9% of 801 ≈ 25% of 800 = 200.

Fast tricks

• Multiply by 5: multiply by 10, then halve. 46 × 5 = 460 ÷ 2 = 230.
• Multiply by 25: multiply by 100, divide by 4. 36 × 25 = 900.
• Squares ending in 5: 65² → 6 × 7 = 42, append 25 → 4225.
• Multiply by 11 (2-digit): 53 × 11 → 5 (5+3) 3 = 583.
• Digit-sum check: use the unit digit of options to eliminate wrong answers quickly.

Caution

Do not approximate when options are very close (e.g., 1024, 1026, 1029). Then calculate exactly.

Analogy

Approximation is like estimating a grocery bill in your head. Items cost ₹49, ₹98 and ₹151 — you think "50 + 100 + 150 = 300" and know you need about ₹300 before the cashier totals it. You only count every paisa when two bills look almost the same.